Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

Estimation of body fatness from body mass index and bioelectrical impedance: comparison of New Zealand European, Maori and Pacific Island children

Objective: To compare percentage body fat (%BF) for a given body mass index (BMI) among New Zealand European, Maori and Pacific Island children. To develop prediction equations based on bioimpedance measurements for the estimation of fat-free mass (FFM) appropriate to children in these three ethnic groups. Design: Cross-sectional study. Purposive sampling of schoolchildren aimed at recruiting three children of each sex and ethnicity for each year of age. Double cross-validation of FFM prediction equations developed by multiple regression. Setting: Local schools in Auckland. Subjects: Healthy European, Maori and Pacific Island children (n = 172, 83 M, 89 F, mean age 9.4 +/- 2.8(s. d.), range 5 - 14 y). Measurements: Height, weight, age, sex and ethnicity were recorded. FFM was derived from measurements of total body water by deuterium dilution and resistance and reactance were measured by bioimpedance analysis. Results: For fixed BMI, the Maori and Pacific Island girls averaged 3.7% lower % BF than European girls. For boys a similar relation was not found since BMI did not significantly influence % BF of European boys ( P = 0.18). Based on bioimpedance measurements a single prediction equation was developed for all children: FFM (kg) = 0.622 height (cm)(2)/ resistance +0.234 weight (kg)+1.166, R-2 = 0.96, s. e. e. = 2.44 kg. Ethnicity, age and sex were not significant predictors. Conclusions: A robust equation for estimation of FFM in New Zealand European, Maori and Pacific Island children in the 5 - 14 y age range that is more suitable than BMI for the determination of body fatness in field studies has been developed. Sponsorship: Maurice and Phyllis Paykel Trust, Auckland University of Technology Contestable Grants Fund and the Ministry of Health.

Evaluation of extractants for estimation of the phytoavailable trace metals in soils

Despite its environmental (and financial) importance, there is no agreement in the literature as to which extractant most accurately estimates the phytoavailability of trace metals in soils. A large dataset was taken from the literature, and the effectiveness of various extractants to predict the phytoavailability of Cd, Zn, Ni, Cu, and Pb examined across a range of soil types and contamination levels. The data suggest that generally, the total soil trace metal content, and trace metal concentrations determined by complexing agents (such as the widely used DTPA and EDTA extractants) or acid extractants (such as 0.1 M HCl and the Mehlich 1 extractant) are only poorly correlated to plant phytoavailability. Whilst there is no consensus, it would appear that neutral salt extractants (such as 0.01 M CaCl2 and 0.1 M NaNO3) provide the most useful indication of metal phytoavailability across a range of metals of interest, although further research is required.

Bioelectrical impedance analysis for the estimation of body composition in rats

Bioelectrical impedance analysis (BIA) was used to assess body composition in rats fed on either standard laboratory diet or on a high-fat diet designed to induce obesity. Bioelectrical impedance analysis predictions of total body water and thus fat-free mass (FFM) for the group mean values were generally within 5% of the measured values by tritiated water ((H2O)-H-3) dilution. The limits of agreement for the procedure were, however, large, approximately +/-25%, limiting the applicability of the technique for measurement of body composition in individual animals.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

A reproducible method for automated extraction of brain volumes from 3D human head MR images

An automated method for extracting brain volumes from three commonly acquired three-dimensional (3D) MR images (proton density, T1 weighted, and T2-weighted) of the human head is described. The procedure is divided into four levels: preprocessing, segmentation, scalp removal, and postprocessing. A user-provided reference point is the sole operator-dependent input required, The method's parameters were first optimized and then fixed and applied to 30 repeat data sets from 15 normal older adult subjects to investigate its reproducibility. Percent differences between total brain volumes (TBVs) for the subjects' repeated data sets ranged from .5% to 2.2%. We conclude that the method is both robust and reproducible and has the potential for wide application.

Estimation of contribution of changes in classic risk factors to trends in coronary-event rates across the WHO MONICA Project populations

Background From the mid-1980s to mid-1990s, the WHO MONICA Project monitored coronary events and classic risk factors for coronary heart disease (CHD) in 38 populations from 21 countries. We assessed the extent to which changes in these risk factors explain the variation in the trends in coronary-event rates across the populations. Methods In men and women aged 35-64 years, non-fatal myocardial infarction and coronary deaths were registered continuously to assess trends in rates of coronary events. We carried out population surveys to estimate trends in risk factors. Trends in event rates were regressed on trends in risk score and in individual risk factors. Findings Smoking rates decreased in most male populations but trends were mixed in women; mean blood pressures and cholesterol concentrations decreased, body-mass index increased, and overall risk scores and coronary-event rates decreased. The model of trends in 10-year coronary-event rates against risk scores and single risk factors showed a poor fit, but this was improved with a 4-year time lag for coronary events. The explanatory power of the analyses was limited by imprecision of the estimates and homogeneity of trends in the study populations. Interpretation Changes in the classic risk factors seem to partly explain the variation in population trends in CHD. Residual variance is attributable to difficulties in measurement and analysis, including time lag, and to factors that were not included, such as medical interventions. The results support prevention policies based on the classic risk factors but suggest potential for prevention beyond these.

Hemichordates and deuterostome evolution: robust molecular phylogenetic support for a hemichordate plus echinoderm clade

Hemichordates were traditionally allied to the chordates, but recent molecular analyses have suggested that hemichordates are a sister group to the echinoderms, a relationship that has important consequences for the interpretation of the evolution of deuterostome body plans. However, the molecular phylogenetic analyses to date have not provided robust support for the hemichordate + echinoderm clade. We use a maximum likelihood framework, including the parametric bootstrap, to reanalyze DNA data from complete mitochondrial genomes and nuclear 18S rRNA. This approach provides the first statistically significant support for the hemichordate + echinoderm clade from molecular data. This grouping implies that the ancestral deuterostome had features that included an adult with a pharynx and a dorsal nerve cord and an indirectly developing dipleurula-like larva.

Comparative analysis of dendritic cell density and total number in commonly transplanted organs: morphometric estimation in normal mice

Dendritic cells (DC) are considered to be the major cell type responsible for induction of primary immune responses. While they have been shown to play a critical role in eliciting allosensitization via the direct pathway, there is evidence that maturational and/or activational heterogeneity between DC in different donor organs may be crucial to allograft outcome. Despite such an important perceived role for DC, no accurate estimates of their number in commonly transplanted organs have been reported. Therefore, leukocytes and DC were visualized and enumerated in cryostat sections of normal mouse (C57BL/10, B10.BR, C3H) liver, heart, kidney and pancreas by immunohistochemistry (CD45 and MHC class II staining, respectively). Total immunopositive cell number and MHC class II+ cell density (C57BL/10 mice only) were estimated using established morphometric techniques - the fractionator and disector principles, respectively. Liver contained considerably more leukocytes (similar to 5-20 x 10(6)) and DC (similar to 1-3 x 10(6)) than the other organs examined (pancreas: similar to 0.6 x 10(6) and similar to 0.35 x 10(6): heart: similar to 0.8 x 10(6) and similar to 0.4 x 10(6); kidney similar to 1.2 x 10(6) and 0.65 x 10(6), respectively). In liver, DC comprised a lower proportion of all leukocytes (similar to 15-25%) than in the other parenchymal organs examined (similar to 40-60%). Comparatively, DC density in C57BL/10 mice was heart > kidney > pancreas much greater than liver (similar to 6.6 x 10(6), 5 x 10(6), 4.5 x 10(6) and 1.1 x 10(6) cells/cm(3), respectively). When compared to previously published data on allograft survival, the results indicate that the absolute number of MHC class II+ DC present in a donor organ is a poor predictor of graft outcome. Survival of solid organ allografts is more closely related to the density of the donor DC network within the graft. (C) 2000 Elsevier Science B.V. All rights reserved.

The HI Parkes All Sky Survey: southern observations, calibration and robust imaging

The acquisition of HI Parkes All Shy Survey (HIPASS) southern sky data commenced at the Australia Telescope National Facility's Parkes 64-m telescope in 1997 February, and was completed in 2000 March. HIPASS is the deepest HI survey yet of the sky south of declination +2 degrees, and is sensitive to emission out to 170 h(75)(-1) Mpc. The characteristic root mean square noise in the survey images is 13.3 mJy. This paper describes the survey observations, which comprise 23 020 eight-degree scans of 9-min duration, and details the techniques used to calibrate and image the data. The processing algorithms are successfully designed to be statistically robust to the presence of interference signals, and are particular to imaging point (or nearly point) sources. Specifically, a major improvement in image quality is obtained by designing a median-gridding algorithm which uses the median estimator in place of the mean estimator.

Estimation of crystalline phase present in the glucose crystal-solution mixture by water activity measurement

The amount of crystalline fraction present in monohydrate glucose crystal-solution mixture up to 110% crystal in relation to solution (crystal:solution=110:100) was determined by water activity measurement. It was found that the water activity had a strong linear correlation (R-2=0.994) with the amount of glucose present above saturation. Difference in the water activities of the crystal-solution mixture (a(w1)) and the supersaturated solution (a(w2)) by re-dissolving the crystalline fraction allowed calculation of the amount of crystalline phase present (DeltaG) in the mixture by an equation DeltaG=846.97(a(w1)-a(w2)). Other methods such as Raoult's, Norrish and Money-Born equations were also tested for the prediction of water activity of supersaturated glucose solution. (C) 2003 Swiss Society of Food Science and Technology. Published by Elsevier Science Ltd. All rights reserved.

Optimal estimation of one-parameter quantum channels

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.